PROOF OF PYTHAGOREANTHEOREM USING

ALGEBRA

Area of Whole Square :

A = (a+b)(a+b)

Area of the smaller (tilted) square :

A= c²

Area of four triangles :

A=4(1/2 ab) = 2ab

The area of the large square is equal to the area of the tilted square and the four triangles.

(a+b)(a+b) = c² + 2ab

a² + 2ab +b² = c² + 2ab Expanding (a+b)(a+b)

a² + b² = c² Subtraction Property of Equality

Proof:

a² + b² = c²

The Pythagorean theorem can be illustrated visually in several ways. One such illustration is shown by the figure on the right. Square A is divided into four regions by two dashed lines that pass through its center. One dashed line is parallel to the left edge of square C, and the other dashed line is parallel to the lower edge of square C. If these four regions and square B are traced and cut out, they can be arranged to cover square C. Try it!

Starting Points for Investigations

1. Draw a right triangle with legs of length 1 inch and 2 inches and a square on each of its sides. (Right angles can be drawn by using the corner of a file card.) Subdivide the larger of the squares on the legs into four regions as described in the figure on the previous slide. Show how these four regions and the square on the other leg can be arranged to exactly cover the square on the hypotenuse.

2. Suppose the smaller of the squares on the legs of a right triangle is subdivided into four regions as described above. Can these regions and the square on the other leg be arranged to cover the square on the hypotenuse?

DOES THIS MAKE THEPYTHAGOREAN

THEOREM FALSE?

NO.

Christine Conlas &Kharelle Mae Naduma